Physical Sciences and Mathematics Commons^™

Methods For Scalar-On-Function Regression, Philip T. Reiss, Jeff Goldsmith, Han Lin Shang, R. Todd Ogden

Philip T. Reiss

Flexible Penalized Regression For Functional Data...And Other Complex Data Objects, Philip T. Reiss

Philip T. Reiss

No abstract provided.

Wavelet-Domain Regression And Predictive Inference In Psychiatric Neuroimaging, Philip T. Reiss, Lan Huo, Yihong Zhao, Clare Kelly, R. Todd Ogden

Philip T. Reiss

An increasingly important goal of psychiatry is the use of brain imaging data to develop predictive models. Here we present two contributions to statistical methodology for this purpose. First, we propose and compare a set of wavelet-domain procedures for fitting generalized linear models with scalar responses and image predictors: sparse variants of principal component regression and of partial least squares, and the elastic net. Second, we consider assessing the contribution of image predictors over and above available scalar predictors, in particular via permutation tests and an extension of the idea of confounding to the case of functional or image predictors. …

Quantile Rank Maps: A New Tool For Understanding Individual Brain Development, Huaihou Chen, Clare Kelly, F. Xavier Castellanos, Ye He, Xi-Nian Zuo, Philip T. Reiss

Philip T. Reiss

We propose a novel method for neurodevelopmental brain mapping that displays how an individual’s values for a quantity of interest compare with age-specific norms. By estimating smoothly age-varying distributions at a set of brain regions of interest, we derive age-dependent region-wise quantile ranks for a given individual, which can be presented in the form of a brain map. Such quantile rank maps could potentially be used for clinical screening. Bootstrap-based confidence intervals are proposed for the quantile rank estimates. We also propose a recalibrated Kolmogorov-Smirnov test for detecting group differences in the age-varying distribution. This test is shown to be …

Cross-Validation And Hypothesis Testing In Neuroimaging: An Irenic Comment On The Exchange Between Friston And Lindquist Et Al., Philip T. Reiss

Philip T. Reiss

The “ten ironic rules for statistical reviewers” presented by Friston (2012) prompted a rebuttal by Lindquist et al. (2013), which was followed by a rejoinder by Friston (2013). A key issue left unresolved in this discussion is the use of cross-validation to test the significance of predictive analyses. This note discusses the role that cross-validation-based and related hypothesis tests have come to play in modern data analyses, in neuroimaging and other fields. It is shown that such tests need not be suboptimal and can fill otherwise-unmet inferential needs.

Varying-Smoother Models For Functional Responses, Philip T. Reiss, Lei Huang, Huaihou Chen, Stan Colcombe

Philip T. Reiss

This paper studies estimation of a smooth function f(x,v) when we are given functional responses of the form f(x, ·) + error, but scientific interest centers on the collection of functions f(·,v) for different v. The motivation comes from studies of human brain development, in which x denotes age whereas v refers to brain locations. Analogously to varying-coefficient models, in which the mean response is linear in x, the “varying-smoother” models that we consider exhibit nonlinear dependence on x that varies smoothly with v. We discuss three approaches to estimating varying-smoother models: (a) methods that employ a tensor product penalty; …

Paradoxical Results Of Adaptive False Discovery Rate Procedures In Neuroimaging Studies, Philip T. Reiss, Armin Schwartzman, Feihan Lu, Lei Huang, Erika Proal

Philip T. Reiss

Adaptive false discovery rate (FDR) procedures, which offer greater power than the original FDR procedure of Benjamini and Hochberg, are often applied to statistical maps of the brain. When a large proportion of the null hypotheses are false, as in the case of widespread effects such as cortical thinning throughout much of the brain, adaptive FDR methods can surprisingly reject more null hypotheses than not accounting for multiple testing at all—i.e., using uncorrected p-values. A straightforward mathematical argument is presented to explain why this can occur with the q-value method of Storey and colleagues, and a simulation study shows that …

Function-On-Scalar Regression With The Refund Package, Philip T. Reiss

Philip T. Reiss

No abstract provided.

Smoothness Selection For Penalized Quantile Regression Splines, Philip T. Reiss, Lei Huang

Philip T. Reiss

Modern data-rich analyses may call for fitting a large number of nonparametric quantile regressions. For example, growth charts may be constructed for each of a collection of variables, to identify those for which individuals with a disorder tend to fall in the tails of their age-specific distribution; such variables might serve as developmental biomarkers. When such analyses are carried out by penalized spline smoothing, reliable automatic selection of the smoothing parameter is particularly important. We show that two popular methods for smoothness selection may tend to overfit when estimating extreme quantiles as a smooth function of a predictor such as …

Semiparametric Methods For Mapping Brain Development, Philip T. Reiss, Yin-Hsiu Chen, Lan Huo

Philip T. Reiss

No abstract provided.

Resampling-Based Information Criteria For Best-Subset Regression, Philip T. Reiss, Lei Huang, Joseph E. Cavanaugh, Amy Krain Roy

Philip T. Reiss

When a linear model is chosen by searching for the best subset among a set of candidate predictors, a fixed penalty such as that imposed by the Akaike information criterion may penalize model complexity inadequately, leading to biased model selection. We study resampling-based information criteria that aim to overcome this problem through improved estimation of the effective model dimension. The first proposed approach builds upon previous work on bootstrap-based model selection. We then propose a more novel approach based on cross-validation. Simulations and analyses of a functional neuroimaging data set illustrate the strong performance of our resampling-based methods, which are …

Introducing Functional Data Analysis To Neuroimaging, And Vice Versa, Philip T. Reiss

Philip T. Reiss

No abstract provided.

Massively Parallel Nonparametrics [Hds 2011 Slides], Philip T. Reiss, Lei Huang

Philip T. Reiss

No abstract provided.

Flexible Dependence Of Functional Responses On Scalar Predictors, Philip T. Reiss, Lei Huang

Philip T. Reiss

No abstract provided.

Extracting Information From Functional Connectivity Maps Via Function-On-Scalar Regression, Philip T. Reiss, Maarten Mennes, Eva Petkova, Lei Huang, Matthew J. Hoptman, Bharat B. Biswal, Stanley J. Colcombe, Xi-Nian Zuo, Michael P. Milham

Philip T. Reiss

Functional connectivity of an individual human brain is often studied by acquiring a resting state functional magnetic resonance imaging scan, and mapping the correlation of each voxel's BOLD time series with that of a seed region. As large collections of such maps become available, including multisite data sets, there is an increasing need for ways to distill the information in these maps in a readily visualized form. Here we propose a two-step analytic strategy. First, we construct connectivity-distance profiles, which summarize the connectivity of each voxel in the brain as a function of distance from the seed, a functional relationship …

Fast, Flexible Function-On-Scalar Regression, With An Application To Brain Development, Philip T. Reiss, Lei Huang

Philip T. Reiss

No abstract provided.

On Distance-Based Permutation Tests For Between-Group Comparisons, Philip T. Reiss, M. Henry H. Stevens, Zarrar Shehzad, Eva Petkova, Michael P. Milham

Philip T. Reiss

Permutation tests based on distances among multivariate observations have found many applications in the biological sciences. Two major testing frameworks of this kind are multiresponse permutation procedures and pseudo-F tests arising from a distance-based extension of multivariate analysis of variance. In this paper we derive conditions under which these two frameworks are equivalent. The methods and equivalence results are illustrated by reanalyzing an ecological data set and by a novel application to functional magnetic resonance imaging data.

Functional Generalized Linear Models With Images As Predictors, Philip T. Reiss, R. Todd Ogden

Philip T. Reiss

Functional principal component regression (FPCR) is a promising new method for regressing scalar outcomes on functional predictors. In this paper we present a theoretical justification for the use of principal components in functional regression. FPCR is then extended in two directions: from linear to the generalized linear modeling, and from univariate signal predictors to high-resolution image predictors. We show how to implement the method efficiently by adapting generalized additive model technology to the functional regression context. A technique is proposed for estimating simultaneous confidence bands for the coefficient function; in the neuroimaging setting, this yields a novel means to identify …

Fast Function-On-Scalar Regression With Penalized Basis Expansions, Philip T. Reiss, Lei Huang, Maarten Mennes

Philip T. Reiss

Regression models for functional responses and scalar predictors are often fitted by means of basis functions, with quadratic roughness penalties applied to avoid overfitting. The fitting approach described by Ramsay and Silverman in the 1990s amounts to a penalized ordinary least squares (P-OLS) estimator of the coefficient functions. We recast this estimator as a generalized ridge regression estimator, and present a penalized generalized least squares (P-GLS) alternative. We describe algorithms by which both estimators can be implemented, with automatic selection of optimal smoothing parameters, in a more computationally efficient manner than has heretofore been available. We discuss pointwise confidence intervals …

Regression When The Predictors Are Images, Philip T. Reiss

Philip T. Reiss

No abstract provided.

Smoothing Parameter Selection For A Class Of Semiparametric Linear Models, Philip T. Reiss, R. Todd Ogden

Philip T. Reiss

Spline-based approaches to nonparametric and semiparametric regression, as well as to regression of scalar outcomes on functional predictors, entail choosing a parameter controlling the extent to which roughness of the fitted function is penalized. In this paper we demonstrate that the equations determining two popular methods for smoothing parameter selection, generalized cross-validation and restricted maximum likelihood, share a similar form that allows us to prove several results common to both, and to derive a condition under which they yield identical values. These ideas are illustrated by application of functional principal component regression, a method for regressing scalars on functions, to …

Regressing Scalar Outcomes On Image Predictors Via Functional Principal Component Regression, Philip T. Reiss

Philip T. Reiss

No abstract provided.

Simultaneous Confidence Bands For The Coefficient Function In Functional Regression, Philip T. Reiss

Philip T. Reiss

No abstract provided.

Inferring Group Differences In Brain Connectivity From Functional Magnetic Resonance Images, Philip T. Reiss

Philip T. Reiss

No abstract provided.

Reliability Of Functional Connectivity Networks: How Can We Assess It?, Philip T. Reiss

Philip T. Reiss

No abstract provided.

Functional Generalized Linear Models With Applications To Neuroimaging, Philip T. Reiss, R. Todd Ogden

Philip T. Reiss

No abstract provided.

Functional Principal Component Regression And Functional Partial Least Squares, Philip T. Reiss, R. Todd Ogden

Philip T. Reiss

Regression of a scalar response on signal predictors, such as near-infrared (NIR) spectra of chemical samples, presents a major challenge when, as is typically the case, the dimension of the signals far exceeds their number. Most solutions to this problem reduce the dimension of the predictors either by regressing on components--e.g. principal component regression (PCR) and partial least squares (PLS)--or by smoothing methods which restrict the coefficient function to the span of a spline basis. This paper introduces functional versions of PCR and PLS, which combine both of the above dimension reduction approaches. Two versions of functional PCR are developed, …

Regression With Signals And Images As Predictors, Philip T. Reiss

Philip T. Reiss

Signal regression and image regression, in which the outcomes are scalars and the predictors are one-dimensional signals or multidimensional images, are of interest in many scientific fields. The principal statistical challenge is how to reduce the dimension of the predictors in what would otherwise be a severely ill-posed problem. A pair of novel methods, functional principal component regression (FPCR) and functional partial least squares (FPLS), combine two existing approaches to the dimension reduction problem: selection of most relevant components, as is done in ordinary principal component regression (PCR) and partial least squares (PLS), and restriction of the coefficient function to …